1 Introduction

Laser ablation (LA) has found its applications in varied fields, such as, thin-film deposition, surgery, fabrication of nanostructures, laser-induced breakdown spectroscopy, etc. [1,2,3]. The physical process of LA and its result depend on various parameters, like fluence and wavelength of the laser, target material, laser pulse duration, etc. [4,5,6,7,8]. Also, the medium in which the ablation is carried out is also very important and hence has been of the chosen subjects of study to specific applications [9, 10]. The field of laser ablation in liquid (LAL) has attracted considerable attention because of its potential applications in the fields like, surgery, fabrication of nanostructures, etc. [11,12,13]. Several experimental works have been reported related to various aspects of LAL, e.g. cavitation bubble, shock waves generated in the medium, etc. [11, 14,15,16]. Parameters, like viscosity of the medium, height of the liquid column, etc. are quite significant in this regard [17,18,19].The evolution and dynamics of oscillating cavitation bubble has been modelled and studied by many groups because of its importance in the process of formation of nanoparticles [20, 21]. The shock waves resulting from the expanding plasma plume in liquid and gas ambient have also been thoroughly explored [22,23,24,25]. Extensive study of the generation and propagation of the shockwave in the medium has also been performed from the point of view of laser-based material processing and surgical methods [26, 27]. The propagation of shock inside the transparent target being ablated has also been studied using the method of photoelastic imaging [28]. Recently, Harilal et al. have reported that shock front acts as a barrier between the plume and the ambient oxygen and resists the oxidation process at the early instants of the plume formation [29]. Masuhara has shown that the shock wave leads to abrupt increase in the concentration of species (proteins and other molecules) in the liquid locally and causes crystallisation [13].

Several diagnostic techniques have been used in the studies reported in the literature related to the observation of the plume, bubble and/or shock wave phenomena in gas/liquid medium. Of all the techniques employed, the most common ones include shadowgraphy, spectrometry and fast imaging using intensified charge-coupled device (ICCD). Shadowgraphy performed in conjunction with fast imaging has been very successful in disseminating the information on the temporal and spatial evolution of the shock front, shock pressure and shock velocity [30]. ICCD-based interferometric technique is one of the most powerful techniques to study the transient properties of expanding plasma [31,32,33]. The advantage is twofold—first, ICCD makes it possible to have good temporal resolution (of the order of ≈ten ns) and second, interferometry gives the whole field (two-dimensional) phase information enabling the generation of the complete map of mass and charge density in the field of view.

In spite of the numerous experimental studies reported in the literature related to LAL, very little attention has been paid to understand the density perturbations of the medium that occur due to the process of ablation. These density perturbations play a crucial role in the implementation of LAL in applied research. Therefore, a detailed quantitative analysis of the whole field mass and electronic charge density perturbation is necessary. To the best of the knowledge of the authors, whole field study of plasma-induced shock wave in liquid media with different densities has not been reported till date. As an attempt to address this lacuna in this field, the present work is concerned with the experimental investigation of the effects of propagation of laser-induced shock wave in liquid media of different densities. Experiments have been performed with water and aqueous solutions of ethylene glycol (EG) with two different concentrations. Using interferometric technique, we have analysed the refractive index (RI) variations over the field of view. Detailed quantitative information of the mass density distribution and the effect of medium density on electronic charge density in the plume region have been obtained by using the RI distribution. The transient evolution of the shock and its effects on the medium have also been studied and reported.

2 Experimental set up

The schematic of the complete experimental set-up has been shown in Fig. 1. Ablation of a copper target (99.9% purity), mechanically polished and chemically cleaned, was performed by the fundamental (1064 nm) of an Nd:YAG laser (Quantel Q-smart 850) with a pulse duration of 6 ns.Footnote 1 The spot size was maintained at 0.5 mm at the target surface. Laser fluence was set to 11 J/cm2 and ablation was performed in a cubical glass chamber (with open top), the walls of which are made up of optical quality glass (BK7) with surface flatness of the order of \(\lambda /10\). All the experiments were set-up with target immersed in liquid and the height of the liquid column was maintained constant at 25 mm. To perform ablation in different liquid media, ethylene glycol (reagent grade) was used in different proportions with DI water to achieve 25 and 50% ethylene glycol aqueous solutions (w/w). It is worth mentioning here that, in general, the phenomenon of laser ablation in liquids (LAL) produces nanoparticles, which in turn may lead to an increase in the density of the liquid medium after a relatively large number of ablation shots. However, in the present work, the possible influence of this effect has been taken care of by using an ablation cell of sufficiently large dimensions (50 × 50 × 60 mm) with the liquid column height of at least 25 mm in the experiments, thereby avoiding any significant changes in the concentration of the liquid medium due to a single shot. Furthermore, fresh liquid after every 20 shots has been used in the experiments, which also ensures that there is no significant accummulation of nanoparticles in the liquid medium.

Fig. 1
figure 1

Schematic drawing of the complete experimental set-up employed for the ablation study

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A laser-based Mach–Zehnder interferometer (MZI) was set up as the non-intrusive diagnostic tool for the mapping of RI field. A 532-nm diode-pumped solid-state (DPSS) laser (Verdi V-5 from Coherent Inc.) was employed as the probe laser. As shown in Fig. 1, mirrors M1 and M2 have been used for steering and for initial alignment of the laser beam. The original laser beam is close to 2 mm in diameter. A beam expander assembly (Thorlabs), comprising of lenses L-1 and L-2 with a pin hole (P) in between, has been used to expand the light beam. The distance between the aperture and the lens is adjustable. The expanded and diverging light beam, as it emerges from the variable aperture, has been collimated into a 20-mm diameter beam using a collimating lens (L2). This collimated beam now acts as the probe beam for the Mach–Zehnder interferometer. The first beam splitter (BS-1) splits the light beam into the two arms of the interferometer: the test arm (BS-1 to M-3 to BS-2), which houses the ablation cell and the reference arm (BS-1 to M-4 to BS-2). The optical components of the interferometer (e.g. beam splitters, mirrors (M-1 and M-2), etc. are of high optical grade (BK 7, Flatness: λ/10).

A chamber (indicated as compensator in the figure) of the same dimensions and material as the ablation chamber and containing the same quantity of experimental liquid has been used as a compensator to equate the optical path lengths of the two arms of the interferometer under reference conditions. The shift in the fringes that occurred due to the changes in RI resulting from the propagation of shock was recorded using a fast gated ICCD camera (4picos from Stanford Computer Optics Inc.) with an integration time of 25 ns.Footnote 2 An interference-based line filter F-1 (centred at 532 nm with a linewidth of 1 nm) has been placed before the camera to allow only the 532-nm beam to pass through it. The ICCD camera has been synchronised with the laser Q-switched output, and the in-built timing generator of the camera has been used to generate the required time delay. The exposure was set equal to 25 ns. The camera has been interfaced with PC using the proprietary frame grabber software provided by Stanford Computer Optics Inc. The ICCD has been calibrated using a grid of known dimension to correlate the pixel size with real physical dimensions in the field of view. A movable stop has been placed in the reference arm of the MZI so as to let the only beam passing through the sample arm fall on the ICCD to record the shadowgraph images.

3 Data reduction

The interferograms recorded have been analysed and the relative phase changes, with respect to the reference interferograms, have been retrieved with the maximum possible accuracy. The principles of windowed Fourier transform (WFT) have been employed for quantitative determination of the phase values [34,35,36]. The authors have thoroughly benchmarked the method and the results can be found in the previously published articles [36,37,38]. Since the shock wave and the plume are axi-symetric, Abel inversion has been used and the whole field phase map has been generated from the interferometric images. A discussion on the non-intrusive diagnostic method employed in the present work and further references may be found in a previously published article that describes the propagation of shock in air ambient [33].

The density of the Ethylene Glycol (EG) has been taken from the standard data sheet available in the literature and the mass was calculated for 25 and 50% (w/w) aqueous solution. The density of the solutions with different proportions of EG was also calculated using this data. The densities for 25 and 50% (w/w) aqueous solutions of EG were found to be 1.0203 and 1.0446 g/cm3, respectively. The density of water is known to be 0.9971 g/cm3 at STP. The RI data for different compositions of aqueous EG solution is available in literature [39]. Fogg et al. reported that the variation of RI with mass fraction of EG in aqueous solution follows a linear trend. Thus, RI for the two concentrations of interest (25 and 50% w/w) was obtained from the linear fit of the data reported by Fogg et al. The estimated values of RI were \(1.357793\) and \(1.382765\), for 25 and 50% aqueous solutions of EG, respectively. The RI for water is known to be 1.3312. These RI data have been used for further calculations.

The number density of medium,\(\rho\) is related to the RI(\(n\)) by Lorentz–Lorenz relation and is expressed as follows [40]:

$$\frac{{n^{2} - 1}}{{n^{2} + 2}} = \frac{\alpha \rho }{3}$$
(1)

Here \(\alpha\) is the molecular polarisibility. \(\rho\) is related to the mass density \(\rho_{\text{m}}\) by the relation,

$$\rho_{\text{m}} = \frac{M}{{N_{\text{A}} }}\rho ,$$
(2)

where \(M\) is the molar mass and \(N_{\text{A}}\) is the Avogadro number. Equations 1 and 2 may be combined together to relate the mass density of the medium to the RI,

$$\rho_{\text{m}} = \frac{3M}{{N_{\text{A}} \alpha }}\frac{{n^{2} - 1}}{{n^{2} + 2}}$$
(3)
$$\alpha = \frac{3M}{{N_{\text{A}} \rho_{\text{m}} }}\frac{{n^{2} - 1}}{{n^{2} + 2}}$$
(3a)

As \(\alpha\) is not known for different concentrations of EG, it was first evaluated from Eq. 3a for the known values of \(\rho_{\text{m}}\) and \(n\) for the different concentrations. The value of \(\alpha\),thus obtained, was used for calculating the mass density corresponding to the different values of \(n\).

The electronic charge density, \(N_{\text{e}}\) in the plasma region was calculated using the relation, for \(\lambda = 532 {\text{nm}}\) [40],

$$n = 1 - \frac{{e_{0}^{2} }}{{8\pi^{2} \varepsilon_{0} m_{\text{e}} c^{2} }}\lambda^{2} N_{\text{e}}$$
(4)

In Eq. 4 above, n is the refractive index, \(\varepsilon_{0}\) is the permittivity of the free space, \(c\) is the speed of light in free space, \(m_{\text{e}}\) is the mass of an electron and \(e_{0}\) is the electronic charge.

In the experiments reported, the possible sources of errors include optical aberrations, small amount of misalignment of the optical elements involved, power stability of the probe laser beam, etc. Also, there is a finite amount of error involved in the estimation of phase values from the recorded interferometric images. The experiments were performed by making wedge fringe arrangement of the interferometer. The errors related to the slight misalignment were minimised by ensuring that the fringes are reasonably straight and parallel to each other, under reference conditions. Further details related to the calculation of errors may be found elsewhere [36, 41, 42]. The maximum possible error in the process of phase estimation was found to be ≈5%. Hence, the maximum possible error in the estimation of absolute values of mass density and electron density come out to be ≈10 and ≈5%, respectively.

4 Results and discussion

The sequence of the interferograms at different time delays has been recorded to observe the dynamics of the shock and the plasma plume that resulted from laser ablation of metal substrate immersed in the liquid media. For quantitative understanding, the interferograms have been converted into refractive index (RI) maps and the change in RI with respect to the background has been converted to the charge density and density perturbations of the medium. The concerned data reduction methodology has already been discussed in detail in the previous section. The complete study has been presented in two sections, namely laser ablation of copper in water and laser ablation of copper in aqueous solutions of ethylene glycol (EG). Two different proportions of EG have been considered; 25% (w/w) and 50% (w/w) aqueous solutions of EG.

4.1 Laser ablation of copper in water

The characteristic propagation of the shockwave in the medium was captured by recording the shadowgraph images at different instants of time. Position of the shock front versus time curve was plotted and curve was fitted to Taylor Sedov model, \(r\left( t \right) = at^{n}\). The dependence was found to be of the form \(t^{0.86}\). The average velocity was determined from this fitted curve as \(v_{\text{avg}} \left( t \right) = \frac{1}{T}\mathop \smallint \limits_{{T_{1} }}^{{T_{2} }} nAt^{n - 1} {\text{d}}t\), with \(T = T_{2} - T_{1}\) and was found to be equal to ~1743 m/s. The position of the shock front versus time curve and the corresponding Taylor Sedov fit has been shown in Fig. 2.

Fig. 2
figure 2

Plot of the position of shock front versus time derived from the shadowgraph images. The corresponding Taylor Sedov fit has been shown and the fit parameters have been tabulated

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Further investigations on shock wave and the plasma plume were carried out by analysing the interferograms recorded at different instants of time. The time-lapsed interferograms have been shown in the left column of Fig. 2. Labels a, b, c, d and e correspond to the time instants of \(t = 2, \;4, \;6, \;8 \;{\text{and}}\; 10\) μs, respectively. It is to be mentioned here that only the representative interferograms have been shown that are evenly spaced in time so that the evolution of the shock can be clearly depicted. It is evident from the interferogram shown in Fig. 2a that just above the ablation point, the fringes are significantly deformed. This bending of the otherwise straight and parallel fringe patterns is due to the strong variation in the RI of the medium in this region, which is attributed to the presence of the plasma plume. As the same region is seen in the subsequent interferograms, the corresponding fringes seem to get straightened because of the changes in plasma parameters with the passage of time. Close to the edges of the deformed fringe pattern, strong opposite shifts are observed (due to the compressed and rarefied media on either sides of the shock front), which clearly define the propagating semi-circular shock front boundary.

The recorded interferograms have been analysed using the methodology discussed in the previous section and the RI map (whole field refractive index distribution) corresponding to every spatial location of the interferogram has been generated. The time sequence of the RI maps corresponding to each interferometric image is shown in the second column of Fig. 3. Two distinct regions are seen in the RI map; one having RI greater than or equal to that of water \((n_{\text{w}} = 1.3312)\) and the other having RI less than that of water. The observed increase in the RI values in some regions with respect to the background (RI of water) is to be attributed to the compression of the medium under the influence of the propagating shock wave. The locus of the points of highest values of RI, which describes a semicircle, is to be identified as the boundary of the shock front in the medium. The density of such regions in all the RI maps has been calculated and the ratio of the calculated density to the background density of water \((\rho_{\text{w}} = 0.9971\; {\text{g}}/{\text{cm}}^{3} )\) has been shown in the third (the rightmost) column of Fig. 3. For calculation of mass density of the medium, only the regions having RI greater than or equal to that of water have been considered. Regions having RI less than that of water appear in the initial time instants and are primarily dominated by the plasma plume. At later instants of time, however, the cavitation occurs and the bubble is formed, which scatters most of the light and is seen to be forming a dark region closer to the target surface. While interpreting the interferograms, this fact has been considered and hence only the interferometric images corresponding to t = 2 and 4 µs have been considered to determine the charge density in the plume. A comparative study of all the three cases has been presented later.

Fig. 3
figure 3

The interferograms (left). RI maps (centre) and the ratio of mass densities (right). The labels a, b, c, d and e correspond to 2, 4, 6, 8 and 10 µs, respectively. In the images shown, one pixel corresponds to a physical dimension of 55 µm

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The mass density calculations have been carried out by making use of Lorentz–Lorenz relation (Eq. 3). It can be seen in the third column of the Fig. 3 that the density at the shock front shows a decreasing trend with time. Since the bulk modulus of water is quite high \((2.2\;{\text{GPa)}}\), a significant compression of the medium is not expected. The densities of the medium at \(t = 2\) μs and \(t = 10\) μs are \(1.00017\) times and \(1.00004\) times the background density, respectively. Although these density variations are not very high, yet these may be seen in quantitative terms in the mass density maps of Fig. 3. Also, it is to be seen that the region of maximum compression is moving away from the centre as the time advances. This may be correlated with the higher axial velocity of the shock front in comparison to its off-axial component. This, in turn, means that the central part of the shock compresses the medium more as compared to the edges and hence loses energy faster. A close observation of Fig. 3c, d reveals that there is a wider region over which the perturbation is prevailing, instead of just the shock front. This is because of the fact that there are waves getting reflected from inside the target and these waves are also contributing to the perturbation. Hence, the RI maps and/or the mass density maps shown in the figure basically represent the resultant of all the wave fronts (primary and reflected). A detailed discussion on this phenomenon is presented later in a different section.

For better clarity on understanding the temporal evolution of the shock front, the density variation across the expansion axis has been analysed. The black horizontal lines drawn in the density ratio maps in Fig. 3 correspond to the horizontal sections across which the density variations have been studied. At \(t = 2\) μs, this line is 2.75 mm above the point of ablation. Similarly, in all the other images, the density variation across the mass density map has been studied at the shock front. These variations have been plotted as a function of lateral dimension and have been shown in Fig. 4. The density variation is the maximum at the initial time and then it keeps decreasing thereafter. Also, the lateral spread of the shock increases and, as expected, the shock energy is found to be spreading outward with time. The dip in the plot corresponding to \(t = 2\) μs may be because of the abrupt change in RI values locally due to the breakdown of water caused by the laser beam. This effect is also reflected in the corresponding RI and mass density maps shown in Fig. 3. At later instants of time, the shock gets reflected from the water–air interface and comes back in the medium. However, these reflected shock waves have not been studied in the present work.

Fig. 4
figure 4

The density of the medium at the planes containing the shock front and perpendicular to the direction of ablating laser beam (x = 12.5 mm represents the ablation site)

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4.2 Laser ablation of copper in aqueous solution of ethylene glycol

Ethylene glycol (EG) has been the one of the most commonly employed heat transfer fluids. Unlike water, EG is more viscous and dense and has extensively been used as the host fluid for metallic nanoparticle suspensions, commonly known as nanofluids [43,44,45]. Among the various methods available for preparing such nanofluids, ablation of the bulk metal in the host fluid itself, i.e. the aqueous solution of EG has been one of the direct approaches. In view of the fact that this method involves laser ablation in liquids, it becomes imperative to develop an understanding of the phenomenon of the laser plasma-induced shock wave propagation in such solutions. In this context, the LAL experiments have been performed in aqueous solutions of EG of two different densities in the present work. Comparisons have been made in terms of the density perturbations in the EG medium with water as the reference fluid. As stated above, the aqueous solutions of EG with two different proportions, 25% (w/w) and 50% (w/w), have been prepared and the characteristic propagation of shockwave was observed by recording shadowgraph images. The velocities of shockwave have been found to be ~1914 m/s for 25% EG solution and ~1986 m/s for 50% EG solution.

Interferometric images corresponding to different instants of time have been recorded to observe the shock propagation through the medium in both the cases. The recorded interferograms have been analysed using the data reduction methodology discussed in the previous section and the corresponding RI maps and mass density distributions have been obtained. The interferograms for both the concentrations of EG have been shown side by side in Fig. 5 to have a clear comparative view. The interferograms shown here are again the representative images, like in the previous case, to give a clear qualitative understanding of the evolution of the shock front. The labels, a, b, c and d correspond to time instants of \(t = 2, 4, 6\) and 8 μs, respectively. In the images shown, the x-axis represents the lateral dimension on the target surface with ablation site at the centre. As indicated in the figure caption, one pixel size corresponds to a physical dimension of 55 µm. It may be seen from the interferograms that the shock front is propagating slightly faster in 50% EG solution, which is in accordance with the difference in the speeds of the shockwave in the two cases, as presented above. The oppositely oriented bends in the fringes closer to the edge of the fringe pattern are because of the compression and the rarefaction of the medium ahead and behind the shock front, respectively. As earlier seen in the case of water, here also, the locus of points with maximum bending of fringes (the regions with maximum change in RI) describes a semicircle, which is the boundary of the forward moving shock front.

Fig. 5
figure 5

Interferograms for 25% EG (w/w) solution (left) and 50% EG (w/w) solution (right). The labels a, b, c and d correspond to 2, 4, 6 and 8 µs, respectively. In the images shown, one pixel corresponds to a physical dimension of 55 µm

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The mass density maps (corresponding to the interferograms shown in Fig. 5) for the two different concentrations of EG have been shown in Fig. 6. The physical dimensions along the x and y directions of the maps shown are the same as that mentioned in Fig. 5. The shock front is clearly visible in these images as the region of high density. These high-density regions are seen to be propagating ahead with the passage of time. Also, it is seen that with the passage of time, the region over which the density is perturbed, increases. For an in-depth analysis of the temporal evolution of the shock front, the density variations across the expansion axis along a given horizontal section have been plotted. This horizontal section has been so chosen that it passes through the region of maximum density perturbation. So, the horizontal section also advances with the passage of time. The plots have been shown in Figs. 7 and 8 for 25 and 50% EG solutions, respectively. It is clearly seen from these figures that with the passage of time, the density at the shock front decreases and the energy gets spread out in the lateral direction, i.e. the region of impact is moving radially outward, like in the case of water.

Fig. 6
figure 6

The ratio of the density of the medium to the background (unperturbed) density at the planes containing the shock front and perpendicular to the direction of ablating laser beam. Left panel is for 25% EG solution and the right panel is for 50% EG solution. One pixel corresponds to a physical dimension of 55 µm

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Fig. 7
figure 7

Density of the medium at the planes containing the shock front and perpendicular to the direction of ablating laser beam for 25% EG solution. Lateral position x = 12.5 mm represents the ablation site

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Fig. 8
figure 8

Density of the medium at the planes containing the shock front and perpendicular to the direction of ablating laser beam for 50% EG solution. Lateral position x = 12.5 mm represents the ablation site

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4.3 Multiple wave fronts in the medium

Unlike the case of gaseous medium, shock-induced mass density perturbations in liquid medium are spread over much wider region as seen in the experimental results discussed in the previous section. This observation is to be attributed to the multiple wave fronts that successively keep surfacing in the field of view after the formation of the primary shock front. As the laser pulse hits the target, rapid expansion of plasma plume leads to the formation of primary shock wave. At the same time, the laser pulse also initiates a stress wave that starts travelling in the target material, a phenomenon which has also been reported by several groups in the past, both experimentally as well as through numerical investigations [28, 46, 47]. The stress wave inside the target gets reflected and transmitted at the target-medium interface, as shown schematically in Fig. 9a. Consequent upon the difference in the acoustic impedance of the two media, a process of successive reflection and transmission takes place leading to the emergence of multiple nearly flat wave fronts in the ambient medium.

Fig. 9
figure 9

a schematic representation of the reflection of the stress wave, b shadowgraph image from water at 8 µs and c corresponding interferogram image

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The acoustic impedance for a medium is defined as \(z_{i} = \rho_{i} v_{i}\), where \(\rho\) is the density of the medium and \(v\) is the velocity of sound in the medium. The suffix \(i\) denotes the media forming the interface. Owing to the fact that the reflected stress wave contains much lesser energy as compared to the primary shockwave, it is relatively weaker in strength. Therefore, it is not very prominent in the recorded interferogram, as may be seen in Fig. 9b. This may also be understood by the fact that the amount of energy that will be transmitted to water ambient from the target surface will be approximately 13.4% (the relation between reflection coefficient \(R\) and the acoustic impedance \(z\) is, R = (z 1 − z 2/z 1 + z 2)2) of the energy of the stress wave. To clearly observe these reflected waves, shadowgraph images were recorded under the same experimental conditions. A representative shadowgraph image has been shown in Fig. 9c where the primary and reflected shock waves are clearly visible. In order to observe the evolution of these reflected waves, the shadowgraph images for water as the ambient environment(from \(t = 2\) μs to \(t = 12\) μs) have been recorded and a few representative images have been shown in Fig. 10. The primary shock front and the first reflected stress wave have been labelled in the images corresponding to \(t = 5\) μs and \(6\) μs (Fig. 10) for clear understanding. The white arrows in the later instants depict the first advancing reflected stress wave. Also there are V-shaped waves present in the medium at the time instants of \(t = 5\) and \(6\) μs on the two sides of the evolving hemispherical shock. Similar observations have also been reported in the past [26, 48]. The velocity of these waves depends on the acoustic impedances of the target and the surrounding medium.

Fig. 10
figure 10

Shadowgraph images depicting primary and successively reflected shock fronts. One pixel corresponds to a physical dimension of 55 µm

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In order to confirm that the flat wave fronts that are visible are indeed the reflected stress waves in the medium, we have correlated the separation between the two consecutive flat wave fronts with the travel time of the sound wave in the target material. Given that the target material is copper, the velocity of sound is known to be 4600 m/s and the average speed of shock in water is 1711 m/s (as calculated from the shadowgraphs in the previous section). The temporal separation between the two consecutive reflected stress wave fronts calculated using these values is in very good agreement with the time taken by the stress wave to travel a round trip inside the target. This has also been confirmed by taking a target of different thickness. Therefore, it is reasonable to consider that the wider region under perturbation, as seen in the RI and also the mass density maps, is a resultant of the cumulative effect of the primary shock wave and the successively reflected stress waves. The position of the first reflected wavefront versus time plot gives the velocity of this front, which is equal to 1727 m/s. This is consistent with the speed of shock wave in water that has been found and discussed in Sect. 4.1 earlier. Similar observations have been made with 25% (w/w) and 50% (w/w) solution of EG in water. Position–time graphs have been plotted for the first reflected shock front for all the cases and have been shown in Fig. 11. Here the speed of the reflected waves comes out to be ~1856 and 1925 m/s, respectively, for 25 and 50% EG solutions which is in close agreement with the values obtained from the data, reported in the previous section.

Fig. 11
figure 11

Position versus time graph for the first reflected shock front for water and aqueous solution of 25 and 50% EG

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4.4 Charge density in the plume

As discussed in Sect. 4.1, the regions which are just above the target surface and close to the point of ablation are dominated by the presence of plasma. The plasma comprises both, positively charged ions as well as the electrons. In addition, there are some neutral particles as well. Both, the ions as well as the electrons contribute towards the change of refractive index. However, the relative contribution of electrons towards the changes in the refractive index field is significantly higher as compared to that of the ionic contribution [49, 50]. Therefore, the effective changes in the refractive index field (a net lowering of refractive index) are observed primarily due to the electronic charge in the regions close to the target surface (just above the point of ablation). This electronic charge density in this plasma plume region has been calculated from the corresponding RI values, which are essentially less than that of the ambient. This idea works well with gasses, but in the case of liquid the metal and water vapour resulting from the ablation form a bubble, commonly known as the cavitation bubble, and it surrounds the plasma region. This bubble leads to significant amount of light scattering, leading to practically very less or no light passing through it. In the case of water, it was seen that the formation of bubble starts at around \(t = 8\) μs, but in the case of more viscous liquids it was observed at the time instants as early as \(t = 4\) μs. Therefore, it becomes difficult to observe the effects of charge once the bubble is formed. The dimension of the bubble is within a few mm for the temporal range over which the data have been recorded. This bubble gives the perception of a dark fringe which is misleading and hence may lead to the wrong estimate of charge density. Thus, here the discussions pertaining to the charge density distribution have been made only for \(t = 2\) and \(4\) μs. For qualitative understanding, the representative charge density maps for water and 25% (w/w) EG have been shown in Fig. 12 for two different instants of time.

Fig. 12
figure 12

Charge density map in the plume region at 2 and 4 µs for water and aqueous solution of 25% EG. In the maps shown, one pixel corresponds to a physical dimension of 55 µm

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With reference to the data shown in Fig. 12, a comparison of the charge density maps retrieved at two different time instants for water (left column) shows a significant reduction in the charge density of the plume over a period of 2 µs. Similar observations are also to be made from the charge density maps shown for 25% EG aqueous solutions (right column). These trends are expected since the charge in the plume region gets quenched with time and the plasma thermalizes. On the other hand, at any given time instant, the charge density in the plume for 25% EG solution is comparatively lower than that seen for the case of water (maps shown in the first row of Fig. 11). This trend of charge density is also seen in the maps corresponding to the time instant of \(t = 4\) μs as well (bottom row). These differences in the charge density maps of the two liquids observed at any given time instant are to be attributed to the fact that in a medium of higher density, the plume thermalizes faster due to the increased number of collisions. Thus, for the same material and the same laser fluence, the charge density dies out faster in the medium with relatively higher density (the EG aqueous solution in the present case). Furthermore, the electron charge density maps shown in Fig. 12 clearly reveal a decreasing trend in the charge density as one moves away from the target surface as well as with the passage of time. Similar trend is also to be seen along the radial direction wherein the charge density can be seen to be rapidly falling at any given instant of time.

For better clarity on the quantitative aspects, a comparison has been made between the charge distributions in the three media. The electronic charge density (determined following the assumption that the laser-produced plasma is not completely ionised) has been plotted as a function of the lateral dimension at a plane that has the maximum charge density (~0.55 mm above the ablation site). These plots have been shown in Fig. 13. It is clearly seen from Fig. 13 that at higher values of the density of the medium, the charge density is low in the plume region for the same instant of time. The observed reduction in the charge density with increase in the density of the medium may be attributed to the higher rates of collision of charges in the plume region because of the stronger confinement effects. This eventually leads to rapid thermalization of plasma. Also, the charge density, for any liquid (water and/or EG solution), decreases with time, as is expected in the case of plume expansion.

Fig. 13
figure 13

Charge density distribution as a function of lateral dimension in the plume region at 2 and 4 µs for water and aqueous solutions of 25 and 50% EG. x = 12.5 mm represents the ablation site

Full size image

Importance of the observations made on the basis of the interferometry-based experiments, as discussed above, can be understood by considering the fact that a range of theoretical studies present in literature suggest that the phenomenon of laser ablation in liquid (LAL) leads to the formation of metal vapour and subsequent condensation of the same. This stage of condensation leads to two competitive and coexisting processes, namely the nucleation (formation of nanocrystals) and nanoparticle growth (adhesion of metal vapour around the nucleation centre). When the plume thermalizes rapidly, the nucleation process dominates and more number of particles are formed, which are smaller in size. On the contrary, if the process of thermalization is relatively slow, it leads to the formation of bigger particles owing to the dominance of the crystal growth process over nucleation. Therefore, the dependence of the plasma life-time on the medium density is crucial from the point of view of monitoring the size control of the nanostructures resulting from ablation of metal in liquid media, a subject which forms the future scope of the present experimental work.

5 Conclusions

Interferometric technique has been employed to perform a detailed time-resolved study of the laser produced plasma-induced shock wave in the liquid media of different densities and the subsequent density perturbation. 2D mapping of the medium and charge densities have been carried out by processing the interferometric images using customised algorithms. The perturbation of the ambient medium (mass) density has been found to be spread over a wider region, in contrast to the observed sharp shock boundary in case of air. This is due to the combined effect of the primary shock wave and the successively emerging stress waves due to multiple reflection from within the target surface. It has been observed that the increase in the medium density speeds up thermalization of plasma and hence leads to a considerable reduction in the charge density in the plume region. Primary findings of the present interferometry-based experiments suggest that the medium density affects the way in which the mass density gets perturbed, an observation that holds importance in a range of practical applications of the phenomenon of laser ablation in liquid.